Method and apparatus for linear optical quantum computing
A method for linear optical quantum computing includes configuring at least two first Greenberger-Horne-Zeilinger (GHZ) states consisting of three photons; configuring at least one second GHZ state consisting of four or more photons by firstly combining the at least two first GHZ states; generating at least one microcluster; forming a plurality of star clusters consisting of four side qubits around the central qubit; configuring Raussendorf-Harrington-Goyal (RHG) lattice by using the plurality of star clusters; and measuring at least one central qubit of the RHG lattice.
1 . A method for linear optical quantum computing comprising:
configuring at least two first Greenberger-Horne-Zeilinger (GHZ) states consisting of three photons;
configuring at least one second GHZ state consisting of four or more photons by firstly combining the at least two first GHZ states;
generating at least one microcluster of type 1 comprising a specific entangled state consisting of three multiphoton qubits defined as (n, m) parity-state encoding for two side qubits and (l, k) parity-state encoding for one central qubit and at least two or more microcluster of type 2 containing a specific entangled state consisting of three multiphoton qubits defined by (n, m) parity state coding for three side qubits, by secondly combining the first GHZ state, the second GHZ state, or a combination thereof;
forming a plurality of star clusters consisting of four side qubits around the central qubit by thirdly combining the at least one microcluster of type 1 and the at least two microclusters of type 2;
configuring Raussendorf-Harrington-Goyal (RHG) lattice by using the plurality of star clusters; and
measuring at least one central qubit of the RHG lattice.
2 . The method for linear optical quantum computing of claim 1 , wherein the step for configuring the at least one second GHZ state includes:
selecting a first photon from any one of the at least two first GHZ states;
selecting a second photon from another first GHZ state; and
performing a first Bell-state measurement (BSM) based on the first photon and the second photon.
3 . The method for linear optical quantum computing of claim 2 , further comprising:
selecting a third photon from any one of the at least two first GHZ states;
selecting a fourth photon from any one of at least one second GHZ state; and
performing a second BSM based on the third photon and the fourth photon.
4 . The method for linear optical quantum computing of claim 2 , wherein the first BSM comprises:
a single photon BSM comprising a plurality of polarizing beam splitters;
a plurality of wave plates; and
a plurality of photon detectors;
wherein the photon detector may include any one of an on-off detector and a single-photon resolving detector.
5 . The method for linear optical quantum computing of claim 1 , wherein H-configuration for determining the quantum state of side qubits in the microcluster of type 1 and type 2 is used, the H-configuration includes a H-configuration of type 1 (HIC) and a H-configuration of type 2 (HIS), the HIC of the microcluster of type 1 is defined by Equation a, and the HIS of the microcluster of type 1 is defined by Equation b,
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6 . The method for linear optical quantum computing of claim 1 , wherein H-configuration for determining the quantum state of side qubits in the microcluster of type 2 is used, the H-configuration includes H-configuration of a type 1 (HIC) and a H-configuration of a type 2 (HIS), the HIC of the microcluster of type 2 is defined by Equation c, and the HIS of the microcluster of type 2 is defined by Equation d,
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7 . The method for linear optical quantum computing of claim 1 , wherein a step for configuring the plurality of star clusters comprises:
performing a first multi-photon Bell-state measurement (multi-photon BSM) based on a first side qubit of the microcluster of type 1 and a second side qubit of any one of the microcluster of type 2; and
performing a second multi-photon BSM based on the third side qubit of the microcluster of type 1 and the second side qubit of another of the microcluster of type 2,
wherein the first side qubits and third side qubits of the microcluster of type 1 and the second side qubits of the microcluster of type 2 are removed through the first multi-photon BSM and the second multi-photon BSM,
wherein the star cluster is composed of first central qubits of the microcluster of type 1, first side qubits and third side qubits of the microcluster of type 2.
8 . The method for linear optical quantum computing of claim 1 , wherein the step for forming the plurality of star clusters includes a concatenated Bell-state measurement (multi-photon BSM) which performs block level BSM n times and performs a single-photon BSM m times for a level BSM of each block when two multiphoton qubits are defined as (n, m) parity state coding.
9 . The method for linear optical quantum computing of claim 1 , wherein the step for configuring the Raussendorf-Harrington-Goyal (RHG) lattice by using the plurality of star clusters comprises:
performing a third multi-photon Bell-state measurement (multi-photon BSM) by using a first side qubit of a first star cluster and a third side qubit of a second star cluster among the plurality of star clusters; and
performing a fourth multi-photon BSM by using a third side qubit of the first star cluster and a first side qubit of the second star cluster.
10 . The method for linear optical quantum computing of claim 1 , wherein the first star cluster is disposed at a center of a corresponding plane constituting the RHG lattice, and the second star cluster is disposed at a center of a line segment constituting the corresponding plane.
11 . The method for linear optical quantum computing of claim 1 , wherein the step for configuring the microcluster of type 1 and type 2 includes at least one of:
selecting a first photon from any one of the at least two first GHZ states, selecting a second photon from another first GHZ state, and performing a first fusion based on the first photon and the second photon;
selecting a third photon from any one of the first GHZ states, selecting a fourth photon from any one of the second GHZ states, and performing a second fusion based on the third photon and the fourth photon; and
selecting a fifth photon from any one of the second GHZ states, selecting a sixth photon from another second GHZ state, and performing a third fusion based on the fifth photon and the sixth photon.
12 . The method for linear optical quantum computing of claim 11 , wherein in cases of m=k=1 for a first H-configuration of the microcluster of type 1 (HIC), n=k=1 for a second H-configuration of the microcluster of type 1 (HIS), or n=m=1 of the microcluster of the type 2, the first fusion, the second fusion, and the third fusion are not performed, and
a single photon Hadamard gate is applied to at least some or all of the photons not participating in the first fusion, the second fusion and the third fusion.
13 . A method for linear optical quantum computing comprising:
determining a combination graph, wherein the combination graph comprises a plurality of vertices representing microclusters and a plurality of lines connecting the vertices, each line corresponding to a single-photon fusion or a Bell-State Measurement;
determining a sequence of a plurality of single photon fusions and a plurality of single photon Bell-state measurements (BSMs) expressed by a shape of the combination graph and one or more lines between the vertices by performing a resource optimization algorithm for the combination graph consisting of a plurality of vertices representing an arbitrary microcluster and lines connecting the vertices;
configuring at least two first Greenberger-Horne-Zeilinger (GHZ) states consisting of three photons based on the shape of the combination graph;
generating at least one microcluster of type 1 including a specific entangled state consisting of three multiphoton qubits defined by (n, m) parity-state encoding for two side qubits and (l, k) parity-state encoding for one central qubit, and at least two or more microclusters of type 2 comprising a specific entangled state consisting of three multiphoton qubits defined by (n, m) parity state coding for three side qubits, based on the sequence of the single photon fusions and the single photon BSMs between the configured first GHZ states;
forming a plurality of star clusters consisting of four side qubits around the central qubit by combining the at least one microcluster of type 1 and the at least two microclusters of type 2;
configuring a Raussendorf-Harrington-Goyal (RHG) lattice by using the plurality of star clusters; and
measuring at least one central qubit of the RHG lattice.
14 . An apparatus for linear optical quantum computing comprising at least one processor, at least one single-photon BSM and at least one multi-photon Bell-state measurement (multi-photon BSM) operating under the control of the processor, wherein the at least one processor includes commands for:
configuring at least two first Greenberger-Horne-Zeilinger (GHZ) states consisting of three photons;
configuring at least one second GHZ state consisting of four or more photons by firstly combining the at least two first GHZ states;
generating at least one microcluster of type 1 comprising a specific entangled state consisting of three multiphoton qubits defined as (n, m) parity-state encoding for two side qubits and (l, k) parity-state encoding for one central qubit and at least two or more microcluster of type 2 containing a specific entangled state consisting of three multiphoton qubits defined by (n, m) parity state coding for three side qubits, by secondly combining the first GHZ state, the second GHZ state, or a combination thereof;
forming a plurality of star clusters consisting of four side qubits around the central qubit by thirdly combining the at least one microcluster of type 1 and the at least two microclusters of type 2;
configuring Raussendorf-Harrington-Goyal (RHG) lattice by using the plurality of star clusters; and
measuring at least one central qubit of the RHG lattice.
15 . The apparatus for linear optical quantum computing of claim 14 , wherein the at least one processor further includes a command for controlling to select a first photon from any one of the at least two first GHZ states, select a second photon from another first GHZ state, and perform a first Bell-state measurement (BSM) based on the first photon and the second photon.
16 . The apparatus for linear optical quantum computing of claim 15 ,
wherein the at least one processor further includes a command for selecting a third photon from any one of the at least two first GHZ states, selecting a fourth photon from any one of at least one second GHZ state; and performing a second BSM based on the third photon and the fourth photon.
17 . The apparatus for linear optical quantum computing of claim 15 , wherein the first BSM includes:
a single photon BSM comprising a plurality of polarizing beam splitters;
a plurality of wave plates; and
a plurality of photon detectors,
wherein the photon detector includes any one of an on-off detector and a single-photon resolving detector.
18 . The apparatus for linear optical quantum computing of claim 14 , wherein H-configuration for determining the quantum state of side qubits in the microcluster of type 1 and type 2 is used, the H-configuration includes a H-configuration of type 1 (HIC) and a H-configuration of type 2 (HIS), the HIC of the microcluster of type 1 is defined by Equation a, and the HIS of the microcluster of type 1 is defined by Equation b,
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wherein H-configuration for determining the quantum state of side qubits in the microcluster of type 2 is used, the H-configuration includes H-configuration of a type 1 (HIC) and a H-configuration of a type 2 (HIS), the HIC of the microcluster of type 2 is defined by Equation c, and the HIS of the microcluster of type 2 is defined by Equation d,
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19 . The apparatus for linear optical quantum computing of claim 14 ,
wherein the at least one processor controls the multi-photon BSM, so that a first multi-photon BSM is performed based on a first side qubit of the microcluster of type 1 and a second side qubit of any one of the microcluster of type 2,
wherein a second multi-photon BSM is performed based on a third side qubit of the microcluster of type 1 and a second side qubit of another one of the microcluster of type 2,
wherein the first side qubits and third side qubits of the microcluster of type 1 and the second side qubits of the microcluster of type 2 are removed through the first multi-photon BSM and the second multi-photon BSM,
wherein the star cluster is composed of a first central qubit of the microcluster of type 1 and first side qubits and third side qubits of the microclusters of type 2.
20 . The apparatus for linear optical quantum computing of claim 14 , wherein the at least one processor controls the multi-photon BSM, so that a third multi-photon BSM is performed based on a first side qubit of a first star cluster and a third side qubit of a second star cluster of the plurality of star clusters, and a fourth multi-photon BSM is performed based on a third side qubit of the first star cluster and a first side qubit of the second star cluster.
21 . The apparatus for linear optical quantum computing of claim 14 , wherein the at least one processor includes:
at least one of a command for selecting a first photon from any one of the at least two first GHZ states, selecting a second photon from another first GHZ state, and performing a first fusion based on the first photon and the second photon;
a command for selecting a third photon from any one of the first GHZ state, selecting a fourth photon from any one of the second GHZ state, and performing a second fusion based on the third photon and the fourth photon; and
a command for selecting a fifth photon from any one of the at least two second GHZ states, selecting a sixth photon from another second GHZ state, and performing a third fusion based on the fifth photon and the sixth photon.
22 . The apparatus for linear optical quantum computing of claim 21 , wherein in cases of m=k=1 for a first H-configuration of the microcluster of type 1 (HIC), n=k=1 for a second H-configuration of the microcluster of type 1 (HIS), or n=m=1 of the microcluster of the type 2, the first fusion, the second fusion, and the third fusion are not performed, and
a single photon Hadamard gate is applied to at least some or all of the photons not participating in the first fusion, the second fusion and the third fusion.